math calculator
Solve triangle sides, angles, area, and perimeter.
Save this page to solve geometric properties of three-sided shapes during math studies or architectural layouts.
Area
6
Formula
Area = sqrt(s(s-a)(s-b)(s-c))Given three sides, the calculator checks triangle validity and uses Herons formula to estimate area.
Step by step
Example
A 3-4-5 triangle has perimeter 12, semi-perimeter 6, and area 6.
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Summary
Calculated Area
6
Total Perimeter
12
Semi-Perimeter
6
Validity Status
Valid Triangle
D3 visualization
Compare the lengths of the three sides of the triangle.
D3 visualization
Overview of calculated perimeter and Heron's formula area.
Guide
A triangle is valid only if the sum of any two sides is strictly greater than the third side. When this condition is met, Heron's formula can determine the area of the triangle without knowing its height.
Heron's formula uses the semi-perimeter (half the perimeter) and side lengths: Area = sqrt(s(s-a)(s-b)(s-c)). It is highly useful in land measurement, construction, and geometry studies.
Heron’s formula
A formula for calculating the area of a triangle given the lengths of its three sides.
Perimeter
The total distance around the boundary of a two-dimensional shape.
It states that for any valid triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
It is half of the perimeter of the triangle, calculated as (a + b + c) / 2.